Hi everyone,
The compound of five tetrahedra is a geometric object that interests me for=
a long time. As a freshman, I carefully drew it using compass and straight=
edge on my notebook. I've always been intrigued by its relation to the dode=
cahedron, the chirality, and its pretty shape. In short, it's my geometric =
crush.=20
So far I haven't seen a twisty puzzle based on this shape. Recently, inspir=
ed by Leslie Le's Super Star, I decided to write a simulator. That's defini=
tely a good motivation for me to learn Java applet programming. It's done a=
nd can be found here:
http://people.bu.edu/nanma/TwistyStar/TwistyStar.html
You may need to upgrade JRE to see it. I call it "Twisty Star" because it's=
a twisty puzzle, and also the shape looks twisted. Some screenshots:
[http://twistypuzzles.com/forum/download/file.php?id=3D30776]
[http://twistypuzzles.com/forum/download/file.php?id=3D30777]
It's a compound of five tetrahedra intersecting with each other. The 20 ver=
tices coincide with the vertices of a dodecahedron. The five tetrahedra are=
colored by five colors.=20
It can be twisted around 20 vertices. Since the cuts are right above the fa=
ces of the tetrahedra, it can be regarded as "face-turning" as well as "ver=
tex-turning". In other words, the dual of this solid is its mirror. So it's=
almost self-dual. Therefore there's a one to one correspondence between th=
e vertices and the faces. Mathematically it's related to the face-turning i=
cosahedra.
The vertex to twist is labeled by a small circle around it, and the moving =
region is highlighted. Even with these assistances, it's not easy to see ho=
w it turns. Sometimes with only one twist away from the solved state, I jus=
t can't find the twist. I haven't solved it yet. For this color scheme, I g=
uess it has multiple solved states, meaning that one can, for example, swap=
the red tetrahedron with the blue one.
I think it's possible to build a physical version. I posted this simulator =
on the Twistypuzzles forum [http://twistypuzzles.com/forum/viewtopic.php?f=
=3D1&p=3D281801] and request the builders over there to consider it. Maybe =
someone will make it someday.
I'd like to thank Melinda, Roice, Jeremy and Brandon for their feedback.=20
Please let me know if you see more glitches.
Have fun solving it!
-- schuma